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The Case Against Algebra
HughPickens.com writes: Dana Goldstein writes at Slate that political scientist Andrew Hacker proposes replacing algebra II and calculus in the high school and college with a practical course in statistics for citizenship. According to Hacker, only mathematicians and some engineers actually use advanced math in their day-to-day work and even the doctors, accountants, and coders of the future shouldn't have to master abstract math that they'll never need. For many math is often an impenetrable barrier to academic success. Algebra II, which includes polynomials and logarithms, and is required by the new Common Core curriculum standards used by 47 states and territories, drives dropouts at both the high school and college levels. Hacker's central argument is that advanced mathematics requirements, like algebra, trigonometry and calculus, are "a harsh and senseless hurdle" keeping far too many Americans from completing their educations and leading productive lives. "We are really destroying a tremendous amount of talent—people who could be talented in sports writing or being an emergency medical technician, but can't even get a community college degree," says Hacker. "I regard this math requirement as highly irrational." According to Hacker many of those who struggled through a traditional math regimen feel that doing so annealed their character while critics says that mathematics is used as a hoop, a badge, a totem to impress outsiders and elevate a profession's status. "It's not hard to understand why Caltech and M.I.T. want everyone to be proficient in mathematics. But it's not easy to see why potential poets and philosophers face a lofty mathematics bar. Demanding algebra across the board actually skews a student body, not necessarily for the better."
How about a course in logic, particularly Boolean logic? I agree, very few people really need to understand logarithms or even polynomials. But learning how to think, and solve problems is important.
The only reason why maths is hard is adults keep telling children that it's hard.
Those who do not learn from commit history are doomed to regress it.
The amount of a language you'd learn in a single class, or even taking a single course every year in high school isn't enough to get you be fluent, or even passable in a second language. There are millions of Canadians as hard data that show you can put students in plenty of classes in a second language without actually learning anything. Unless you have an immersion program where people are forced to use the language, then people aren't going to learn the language at all.
Anthropic principle: We see the universe the way it is because if it were different we would not be here to see it.
I wonder how can one develop the proper reasoning need for a philosopher without the formal Logic training that is algebra.
Linux is for people who don't mind RTFM.
It sounds like they only want to replace the higher level algebra stuff, so the base would still be there as a necessary foundation for studying statistics.
This sounds like a great idea. Statistics are regularly, routinely abused to mislead people. As a life skill for the general population, statistics is going to be much more useful than advanced algebra or calculus.
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SJW, n: "Someone I don't like, and by the way I'm a fuckwit" - AC
"I actually found this funny"
Funny in a very sad way.
So... our solution to increasing drop out rates is to make the curriculum simpler? Idiocy! (That should be pronounced 'Idiocracy') Its true that I'm not calculating trajectories or finding the surface area of unusual shaped solids defined by funky formulas -- most of that knowledge has been lost to me over the years. I've retained maybe 1/3 of my leet-math-skills(tm). If all we teach is basic algebra and some statistics and there is a SIMILAR loss of retention in students then what will they have left 10-20 years later? I fear maybe barely enough to balance a checkbook. Hell, basic cashiers don't even have to do basic math any more -- they just need to know how to push buttons and read numbers.
Very well said. There is a tremendous bias against jobs that involve working with your hands and far too many people are encouraged to "go to college" in order to obtain some apocryphal "white collar" career. I would say that a lot of the IT problems many companies have originate with this blue collar bias, with the belief that IT employees are somehow not quite white collar.
I had a conversation with the maintenance supervisor at a client who told me about his son. In the top 10% of his class in high school, he told the school counselor he didn't want to go to college. The counselor requested a meeting with his dad and basically beat him up for not making him go to college (the kid ended up getting some kind of 2 year drafting education, and works for a kitchen equipment maker travelling to job sites to review kitchen construction plans to make sure the planned designs and installations will work -- the guy said he makes close to 100k).
As far as I can tell, all the "go to college" rhetoric has done is build college administration empires, make oodles of money for the student loan industry and probably dumb down traditional academic courses that vocationally-minded students have no interest in.
And what's the end game, exactly? $100k in a debt so you can make coffee? We've flooded the market with half-educated college graduates aspiring to a mythical middle class lifestyle that's becoming increasingly unobtainable even by well educated graduates.
One thing that kind of counts against a lot of skilled trades is the abysmal, old-school hostile management-labor relationship. I worked closely with journeyman electricians as my last job and while the benefits they had seemed great, the work environment seemed really unpleasant. Draconian, authoritarian management schemes, forced overtime and work rules that make a $20k a year cubical job seem pleasant.
According to the description, he's advocating scrapping the teaching of logarithms. Will the kids be taught that everything has a rectangular distribution?
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Meanwhile, apparently the number of American teens who excel at advanced math has surged... Not to mention, considering algebra and trigonometry "advanced" is just ludicrous.
Algebra 1 is sufficient for formal logic, though. He isn't saying to eliminate all algebra. Frankly, stats would not be my choice as a follow-up, but rather a combination of critical thinking courses and civics. Society would likely benefit greatly from more people being involved and more capable of separating their emotions from their important decisions.
Basic algebra, trigonometry and calculus are not difficult. If the students can't handle it, they are dumb, even if that doesn't please you. End of the story.
Not difficult for YOU, you mean.
I love math, and I always aced math classes. I LOVED differential equations in college. I tried to transfer my love of math and science to my children. Two children who are good at math, and they were valedictorians. Another is a high school English teacher. :) I have a fourth child who tested as gifted, but she has extreme difficulty with math at the level of Algebra I and beyond. She repeated Agebra I three times in high school; I finally had to get a variance from the state just so she could graduate. She has taken College Algebra three times and done poorly at it, despite tutoring. She does poorly at foreign languages, failing both Spanish and German. However, she does well in her other classes -- top of the class in other subjects.
So, she's not dumb, but she has some kind of learning disability in math and language. Perhaps some kind of a trade school that specializes in her talents would have been a better option -- but the career she is shooting for demands a college degree, so she perseveres.
He suggests dropping Algebra II as a requirement. The first two statistics courses I took in college had only Algebra I as a prerequisite.
As someone who actually taught Algebra II in high school (years ago), and who taught it one year in a lower-class mostly minority school district, I'll offer a few observations:
(1) I think a stats course would be a great alternative for many students compared to a second year of algebra.
(2) Algebra II was in fact a barrier for many students. There was a high rate of students failing and dropping the course. (At that time, in the state I was teaching, it wasn't strictly required for graduation -- but it was strongly recommended.)
(3) However, the problems with algebra II often start with teaching in algebra I. The algebra I and "pre-algebra" classes tend to be the "dumping ground" in many school districts for less qualified teachers. Teachers with real math degrees often were required to take stuff a lot more complicated than high school, and they often find it barely interesting to teach calculus or pre-calculus. So, in most places the qualified teachers who understand math often teach those upper-level courses, and the random coaches and people who barely passed the math certification test end up teaching algebra I. (There are serious teacher shortages in many places in the US, particularly for secondary math and science.)
(4) As an algebra II teacher, I was confronted with many students who had had a substitute teacher in algebra I for a large portion of the year. The district simply couldn't find qualified teachers to fill those classrooms. The students knew nothing. The previous algebra II teacher (a really smart woman) quit in the middle of the year, because she recognized this and wanted to either (a) send the students back to algebra I since they shouldn't have passed in the first place or (b) require many of the students to come in for mandatory tutoring outside of school hours. She wanted to help the students and was willing to take her own personal time to fix this problem. But the administration said neither was possible under state law, since the students already "had credit" for algebra I. After fighting the battle for a while, she quit.
(5) In many states, algebra teachers are forced to make stupid curriculum choices due to state-mandated curricula. I haven't looked at the new Common Core approaches and what they require, but I can tell you from my experience that we often were required to spend a ridiculous time on stuff that might have been useful for scientists and engineers headed for college in the 1950s, but these skills were much less relevant with modern calculators and computers.
(6) In general, most state curricula have tended to emphasize symbolic manipulation over real-world application (which often comes with true understanding). I was forced to spend many weeks going over how to put conic section equations into standard form, but there was nothing in state guidelines asking teachers to spend time on much more relevant real-life stuff, like applications of basic exponential equations to calculating loan terms or mortgages, investments, etc. When at some point I realized that only 2 of the 140 students I was teaching that year knew what the term "compound interest" meant, I actually abandoned the state standards for a couple weeks because I thought it was my moral responsibility to teach these kids some actual skills that could be useful in personal finance -- this would likely be the last class that many of them would ever take in their lives.
(7) Given the poor teaching and introduction to basic abstractions like variables that students receive in pre-algebra and algebra I in many schools, the only way to "teach algebra II" is learning stupid abstract algorithms for symbolic manipulation, which are generally forgotten a few weeks later. The understanding of basic algebra is often so poor that you really can't teach algebra II on a deep level
You're going to have to do a lot of convincing to get anyone to believe that people do math because they enjoy it.
Indeed, the idea of maths has become so perverted that people don't even seem to believe that it is an enjoyable activity in its own right. It's so far perverted that despite a rich history of people doing maths for curiosity and fun, you still find it unbelievable even though evidence abounds.
Maths for its own sake dates back to the Babylonians, who pretty much invented maths.
Math is a means to an enjoyable end.
It is, and always has been also an enjoyable end in itself. Here are some quotes by Hardy:
"A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas."
"I am interested in mathematics only as a creative art."
"The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics."
SJW n. One who posts facts.
AFAICS, most people who think they understand statistics don't. What they understand is how to apply some rote rules to data that all too often shouldn't have those particular rules used on it.
This is undoubtedly true. I can completely get behind the author's notion that more people need to understand statistics. When I was in basic bio-medical research it was appalling how often statistics were not properly applied. Mostly it was "run a student T test and look for P values of .05 or less" with no further analysis. It was not at all uncommon to do a paper at journal club that had serious problems with their data, but had nice looking numbers supporting statistical significance.
I include myself, of course. I had enough statistics to know how to apply the formulas and to spot some basic issues, but until I collaborated with a real PhD statistician I had no idea just how bad it was. She basically showed me that I had no idea what I was doing, even though I was following the industry standard protocols. And she showed me just how awful the statistics were in most of the work I was reading. At least I think she did. I don't know. Most of what she was talking about I had to take on faith..... because, you know.... my knowledge of statistics isn't that advanced.